Prime factorization of $$$3213$$$

Find the prime factorization of $$$3213$$$.

Start with the number $$$2$$$.

Determine whether $$$3213$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$3213$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3213$$$ by $$${\color{green}3}$$$: $$$\frac{3213}{3} = {\color{red}1071}$$$.

Determine whether $$$1071$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1071$$$ by $$${\color{green}3}$$$: $$$\frac{1071}{3} = {\color{red}357}$$$.

Determine whether $$$357$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$357$$$ by $$${\color{green}3}$$$: $$$\frac{357}{3} = {\color{red}119}$$$.

Determine whether $$$119$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$119$$$ is divisible by $$$5$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$7$$$.

Determine whether $$$119$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$119$$$ by $$${\color{green}7}$$$: $$$\frac{119}{7} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$3213 = 3^{3} \cdot 7 \cdot 17$$$.

The prime factorization is $$$3213 = 3^{3} \cdot 7 \cdot 17$$$A.